A363520 Product of the divisors of n that are < sqrt(n).

1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 6, 1, 2, 3, 2, 1, 6, 1, 8, 3, 2, 1, 24, 1, 2, 3, 8, 1, 30, 1, 8, 3, 2, 5, 24, 1, 2, 3, 40, 1, 36, 1, 8, 15, 2, 1, 144, 1, 10, 3, 8, 1, 36, 5, 56, 3, 2, 1, 720, 1, 2, 21, 8, 5, 36, 1, 8, 3, 70, 1, 1152, 1, 2, 15, 8, 7, 36, 1, 320, 3, 2, 1

Offset: 1

Author

Wesley Ivan Hurt, Jun 07 2023

Keywords

• nonn
• easy

Examples

			The product of divisors of 16 that are < sqrt(16) = 4 is 1*2 = 2, so a(16) = 2.
		

Crossrefs

Cf. A000196, A010052, A072499, A363521.

Cf. A070039 (sum of those divisors).

Programs

Mathematica

a[n_] := Times @@ Select[Divisors[n], #^2 < n &]; Array[a, 100]

PARI

a(n) = vecprod(select(x->(x^2Michel Marcus, Jun 08 2023

Formula

a(n) = Product_{d|n, d

a(n) = Product_{k=1..floor(sqrt(n-1))} k^c(n/k), where c(m) = 1-ceiling(m)+floor(m).

a(n) = A072499(n)/A000196(n)^A010052(n) for n>=1.

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